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Conformal properties of the topological gravitational terms in $D=2$, $D=4$and $D=6$ are discussed. It is shown that in the last two cases the integrandsof these terms, when being settled into the dimension $D-1$ and multiplied by ascalar, become conformal invariant. Furthermore we present a simple covariantderivation of the Paneitz operator in $D=4$ and formulate two generalconjectures concerning the conformal properties of topological structures ineven dimensions.

On the conformal properties of topological terms in even dimensions